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ROUGH SET
Published in Kumar S. Ray, Soft Computing and Its Applications, Volume One, 2014
Rough set philosophy is based on the concept that with every object of the universe of discourse some information (data and knowledge) is associated. For instance, if objects ate patients suffering from a certain disease, symptoms of the disease form information about patients. Objects characterized by the same information are indiscernible (similar) in view of the available information about them. Thus, the indiscernibility relation is generated, which is the essence of rough set theory. Any set of all indiscernible (similar) objects is called an elementary set, which forms a basic granule (atom) of knowledge about the universe. Any union of some elementary sets is referred to as a crisp (precise) set, otherwise the set is rough (vague). Each rough set has boundary-line cases, that is, objects, which cannot be with certainty classified, by employing the available knowledge, as members of the set or its complement. Obviously, rough sets, in contrast to precise sets, cannot be characterized in terms of information about their elements. With any rough set a pair of precise sets, called the lower and the upper approximation of the rough set, is associated. The lower approximation consists of all objects, which surely belong to the set and the upper approximation contains all objects, which possibly belong to the set. The difference between the upper and lower approximation constitutes the boundary region of the rough set. Approximations are fundamental concepts of rough set theory [213, 214, 215].
Soft Computing
Published in Vivek Kale, Digital Transformation of Enterprise Architecture, 2019
The rough set philosophy is founded on the assumption that we associate some information (data and knowledge) with every object of the universe of discourse. Objects, which are characterized by the same information, are indiscernible in view of the available information about them. The indiscernibility relation generated in this way is the mathematical basis for the rough set theory. Any set of all indiscernible objects is called an elementary set, and forms a basic granule of knowledge about the universe. Any set of objects being a union of some elementary sets is referred to as crisp or precise set otherwise the set is rough (imprecise or vague). Consequently, each rough set has boundary-line cases (i.e., objects), which cannot be classified with complete certainty as members of the set. The general procedure for conducting rough set analysis consists of the following: Data preprocessingData partitioningDiscretizationReduct generationRule generation and rule filteringApplying the discretization cuts to test datasetScore the test dataset on the generated rule set (and measuring the prediction accuracy)Deploying the rules in a production system
Rough-fuzzy Case Generation
Published in Sankar K. Pal, Pabitra Mitra, Pattern Recognition Algorithms for Data Mining, 2004
Indiscernibility relation reduces the data by identifying equivalence classes, i.e., objects that are indiscernible, using the available attributes. Only one element of the equivalence class is needed to represent the entire class. Reduction can also be done by keeping only those attributes that preserve the
Estimation of raw silk quality using rough set theory
Published in The Journal of The Textile Institute, 2022
Niharendu Bikash Kar, Anindya Ghosh, Subhasis Das, Debamalya Banerjee
The philosophy of rough set is founded on the basis of assumption that with every object of the universe of discourse some information (data, knowledge) is associated. Objects characterized by the same information are indiscernible (similar) in view of the available information about them. The indiscernibility relation is the mathematical basis of rough set theory and is considered as a relation between two objects or more where all the values are identical in relation to a subset of considered attributes. The indiscernibility relation is intended to express the fact that due to the lack of knowledge it is unable to discern some objects employing the available information. Approximations is another important concept in rough set theory, being associated with the meaning of the approximations in topological operations (Wu et al., 2004).
A Data Mining Approach for Developing Online Streaming Recommendations
Published in Applied Artificial Intelligence, 2021
Shu-Hsien Liao, Retno Widowati, Hao-Yu Chang
Rough set theory (RST) was introduced by Pawlak in the 1980s (Pawlak 1982, 2002) as a mathematical approach to aid decision-making in the presence of uncertainty. The rough set philosophy assumes that for every object there is associated a certain amount of information (data, knowledge), expressed by means of some attributes used for the object’s description. Objects having the same description are indiscernible (similar) with respect to the available information. The indiscernibility relation thus generated constitutes the mathematical basis of RST. It induces a partition of the universe into blocks of indiscernible objects, called elementary sets that can be employed to build knowledge about a real or abstract world. The use of the indiscernibility relation results in information granulation (Greco, Matarazzo, and Slowinski 2001). In other words, when the available knowledge is employed, boundary-line cases cannot be properly classified. Therefore, rough sets can be considered as uncertain or imprecise as illustrated in the following (Liao and Chang 2016).